The best approximation of closed operators by bounded operators in Hilbert spaces
We solve the problem of the best approximation of closed operators by linear bounded operators in Hilbert spaces under assumption that the operator transforms orthogonal basis in Hilbert space into an orthogonal system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for mult...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2022-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/6161 |
| _version_ | 1797205788775677952 |
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| author | V.F. Babenko N.V. Parfinovych D.S. Skorokhodov |
| author_facet | V.F. Babenko N.V. Parfinovych D.S. Skorokhodov |
| author_sort | V.F. Babenko |
| collection | DOAJ |
| description | We solve the problem of the best approximation of closed operators by linear bounded operators in Hilbert spaces under assumption that the operator transforms orthogonal basis in Hilbert space into an orthogonal system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for multiple closed operators is established. We also demonstrate application of these results in concrete situations: for the best approximation of powers of the Laplace-Beltrami operator on classes of functions defined on closed Riemannian manifolds, for the best approximation of differentiation operators on classes of functions defined on the period and on the real line with the weight $e^{-x^2}$, and for the best approximation of functions of self-adjoint operators in Hilbert spaces. |
| first_indexed | 2024-04-24T08:56:42Z |
| format | Article |
| id | doaj.art-58aa84eb46c04699a42f7a03feeaf55c |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:42Z |
| publishDate | 2022-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-58aa84eb46c04699a42f7a03feeaf55c2024-04-16T07:12:26ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102022-12-0114245346310.15330/cmp.14.2.453-4635340The best approximation of closed operators by bounded operators in Hilbert spacesV.F. Babenko0N.V. Parfinovych1D.S. Skorokhodov2Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, UkraineOles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, UkraineOles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, UkraineWe solve the problem of the best approximation of closed operators by linear bounded operators in Hilbert spaces under assumption that the operator transforms orthogonal basis in Hilbert space into an orthogonal system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for multiple closed operators is established. We also demonstrate application of these results in concrete situations: for the best approximation of powers of the Laplace-Beltrami operator on classes of functions defined on closed Riemannian manifolds, for the best approximation of differentiation operators on classes of functions defined on the period and on the real line with the weight $e^{-x^2}$, and for the best approximation of functions of self-adjoint operators in Hilbert spaces.https://journals.pnu.edu.ua/index.php/cmp/article/view/6161best approximation of operatorsstechkin problemkolmogorov-type inequalitiesself-adjoint operatorlaplace-beltrami operatorclosed operator |
| spellingShingle | V.F. Babenko N.V. Parfinovych D.S. Skorokhodov The best approximation of closed operators by bounded operators in Hilbert spaces Karpatsʹkì Matematičnì Publìkacìï best approximation of operators stechkin problem kolmogorov-type inequalities self-adjoint operator laplace-beltrami operator closed operator |
| title | The best approximation of closed operators by bounded operators in Hilbert spaces |
| title_full | The best approximation of closed operators by bounded operators in Hilbert spaces |
| title_fullStr | The best approximation of closed operators by bounded operators in Hilbert spaces |
| title_full_unstemmed | The best approximation of closed operators by bounded operators in Hilbert spaces |
| title_short | The best approximation of closed operators by bounded operators in Hilbert spaces |
| title_sort | best approximation of closed operators by bounded operators in hilbert spaces |
| topic | best approximation of operators stechkin problem kolmogorov-type inequalities self-adjoint operator laplace-beltrami operator closed operator |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/6161 |
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